Problem: As you very well know, this year's funkiest numbers are so called triangular numbers (that is, integers that are representable as <image>, where k is some positive integer), and the coolest numbers are those that are representable as a sum of two triangular numbers.

A well-known hipster Andrew adores everything funky and cool but unfortunately, he isn't good at maths. Given number n, help him define whether this number can be represented by a sum of two triangular numbers (not necessarily different)!

Input

The first input line contains an integer n (1 ≤ n ≤ 109).

Output

Print "YES" (without the quotes), if n can be represented as a sum of two triangular numbers, otherwise print "NO" (without the quotes).

Examples

Input

256


Output

YES


Input

512


Output

NO

Note

In the first sample number <image>.

In the second sample number 512 can not be represented as a sum of two triangular numbers.

Solution (in PYTHON3):

Solution:
n=int(input())
posi=int(n**0.5)
if posi*(posi+1)==n:
    print("YES")
else:
    value=n*2
    i,j=posi,posi
    k=int(value**0.5)
    while (i>=1 and j<=k):
        summ=i*(i+1)+j*(j+1)
        if summ==value:
            break
        elif summ>value:
            i-=1
        else:
            j+=1
    if summ==value:
        print("YES")
    else:
        print("NO")